No. Payments which a claimant (or his/her dependants) is entitled to under the Agreement are completely separate from those payable as a result of the EC Regulations on Social Security. Any benefit already in payment, or subsequently made, under EC regulations will not be affected by any payment made under the terms of the Agreement.
A person can of course receive payment under both the EC Regulations and this Agreement, if he/she worked for example in Ireland, Austria and another EC Member State, but the calculation of pension amounts under the Agreement will not take account of periods of work in the relevant EC State.